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Abstract

Based on the generalized Lorenz-Mie theory (GLMT), this paper reveals, for the first time in the literature, the principal characteristics of the optical forces and radiation pressure cross-sections exerted on homogeneous, linear, isotropic and spherical hypothetical negative refractive index (NRI) particles under the influence of focused Gaussian beams in the Mie regime. Starting with ray optics considerations, the analysis is then extended through calculating the Mie coefficients and the beam-shape coefficients for incident focused Gaussian beams. Results reveal new and interesting trapping properties which are not observed for commonly positive refractive index particles and, in this way, new potential applications in biomedical optics can be devised.

Figures (15)

Normalized (over nmP/c) individual transverse force Fy as a function of both θi and np for a circularly polarized ray over (a) a PRI and (c) a NRI particle. The difference observed between these two cases leads to new trapping phenomena for nrel < 0. (b) and (d) are the contour plots of (a) and (c), respectively.

(a) Ftransverse as a function of both nrel and r for a PRI particle under the influence of a focused Gaussian beam with w0 = 1000 nm. The particle has a radius a = 10λ, where λ = 1064 nm is the wavelength of the beam. When nrel = 1, Ftransverse is always zero, as expected. (b) The contour plot of (a). Arbitrary units are adopted.

(a) Ftransverse as a function of both nrel and r for a NRI particle under the influence of the same laser beam and electromagnetic parameters as in Fig. 3. (b) The contour plot of (a). The same arbitrary units of Fig. 3 are adopted.

Real (solid, red) and imaginary (dashed, blue) parts of the Mie scattering coefficient an as a function of the size parameter x for nrel = 1.33 and (a) n = 1, (b) n = 4, (c) n = 9 and (d) n = 16. In the framework of the GLMT, the coefficients an and bn modulates the phase and amplitude of the scattered fields.

Real (solid, red) and imaginary (dashed, blue) parts of the Mie coefficient an as a function of x for a NRI particle with nrel = −1.33 and (a) n = 1, (b) n = 4, (c) n = 9 and (d) n = 16. Different phase and amplitudes are observed in comparison with Fig. 5, so that the scattered fields will also be different.

(a) Cpr,z for several values of nrel assuming a PRI particle with radius a = 3.75 μm immersed on a focused Gaussian beam with λ = 0.3682 μm and w0 = 1.8 μm. The same relative refractive indices were used in (b) for a NRI particle with the same radius as (a). The beam is shifted along its optical axis, i.e., x0 = y0 = 0.

(a) Cpr,x for several diameters of a PRI particle with nrel = 1.5. The beam is shifted along x with y0 = z0 = 0, x0 being the transverse distance between the optical axis and the centre of the particle. (b) The NRI analogue with nrel = −1.5.

(a) Cpr,y for several diameters of a PRI particle with nrel = 1.5. The beam is shifted along y with x0 = z0 = 0, y0 being the transverse distance between the optical axis (beam waist centre) and the centre of the particle. (b) The NRI analogue with nrel = −1.5.